Prepare a grill or large grill pan for high heat.
Put the tomatoes, onion, and lemon on a baking sheet. Brush with 1 tablespoon of oil and sprinkle liberally with salt and pepper. Lightly oil the grill grates.
Arrange the tomatoes, onion and lemon cut-sides down on the grill. Cook until charred in spots, rotating the tomatoes and onion slices as needed to ensure even cooking, 6 to 8 minutes. Transfer the grilled vegetables and lemon to the same baking sheet that they were on before. Allow to cool 5 minutes. Leave the grill on high heat
Combine the tomatoes and onions in a blender along with the juice of half of the grilled lemon, Worcestershire sauce, honey, horseradish, hot sauce and 1 tablespoon oil. Blend until smooth with the texture of tomato puree. Season with 1 teaspoon salt and 1/4 teaspoon pepper. Pour into a small serving bowl and reserve.
Toss the shrimp with the remaining tablespoon oil and sprinkle liberally with salt and pepper. Grill until lightly charred in spots on both sides and just cooked through, 2 to 3 minutes total. Transfer the shrimp to a large platter and serve with the reserved grilled tomato cocktail sauce. Cut the remaining grilled lemon into wedges and serve on the side.
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